There are two ways to use them depending on the density of the filter.
I typically recommend a 3-stop ND filter as a good choice for an initial filter because it's fairly versatile and most people who are interested in buying ND filters will probably also have or want a circular polarizer -- and the polarizer usually stills "about" 2 stops of light on it's own. That means if you sort-of have a 2-stop "ND" (even though it's really a polarizer), the 3-stop ND cuts half the light again beyond the 2 stops of a CPL, and if you stack them you get 5 stops.
Regardless... all the filter does is change your shooting circumstances. Suppose this is a 3 stop filter. (density level of 0.9 -- because each ".1" of density blocks 1/3rd stop of light). Your camera should meter three stops less light when the filter is on vs. what it meters when the filter is off.
A "sunny 16" exposure of a fountain with no filter at all would be ISO 100, f/16, and 1/100th. With the filter on the camera, that same shot should work at ISO 100, f/16, and 1/13th. That'll cause some blur in the fountain... not a ton. If you bump up the f-stop to f/22 then you can bring the shutter down to 1/6th -- doubling the blur. Stack a CPL on and you can get 2 more stops slower (probably) so now you're down to 2/3rds second (0"6) exposure. And keep in mind... that's in full-mid day sun. Shoot in early morning or late evening and you can do MUCH better.
I have used ND filters when I want to shot outdoors, with shallow DoF, _and_ I want to use flash for fill. Let's pick on the Sunny 16 example again... this time I'm shooting a portrait where I want a deliberately blurred background so f/16 is no good... assume we decide to open up to f/4. That's 4 stops. So now we have to compensate on the shutter by going 5 stops faster... or 1/1600th sec). While the camera can deal with 1/1600th, the flash can't sync at that speed. I can take my shutter up to 1/200th and then use 3 stops of ND for a total of 4 stops worth of compensation and now I'm not beyond the flash sync speed (if you have flash that supports your camera TTL system and also support "high speed sync" you can also solve the problem that way.)
The 10-stop ND filters (density level of 3.0) are also popular when you _really_ want to increase the shutter time. But there's a problem... the filter is so dark that you can hardly see a thing and you can't see to frame & focus the shot. So these filters call for a different strategy.
1) You MUST have a tripod for these long exposures - put camera on tripod.
2) Frame, focus, and meter the shot.
3) Switch lens to manual focus mode.
4) Dial in the exposure as metered by the camera WITHOUT the filter, but dial the shutter speed (you could do part of it with aperture but most people are trying to make the longest shutter exposure possible) back to slow down the shutter by the full 10 stops.
5) Thread the 10-stop ND filter onto the camera -- being CAREFUL not to accidentally alter your lens' focus as you do.
6) Take the shot.
E.g. a "Sunny 16" exposure at ISO 100, f/16, and 1/100th can be slowed down to 10 full seconds -- and you'll get a LOT of blur in 10 seconds (and imagine what you can do in dimmer lighting.)
A 10-stop filter can also make moving objects disappear. Suppose I'm taking the photo of my "fountain" and, in the middle of the shot, some tourist walks right through the frame. In a 10 second exposure... as long as they keep moving and don't pause, they wont actually show up in the image.
With a 10 stop filter you will be putting it on and off the camera a lot -- so much that if you do this regularly, you might even want a slide-in type filter instead of a screw-on filter.
